tasks a-s

Task/Catalan-numbers/PicoLisp/catalan-numbers.l

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+# Factorial
+(de fact (N)
+   (if (=0 N)
+      1
+      (* N (fact (dec N))) ) )
+
+# Directly
+(de catalanDir (N)
+   (/ (fact (* 2 N)) (fact (inc N)) (fact N)) )
+
+# Recursively
+(de catalanRec (N)
+   (if (=0 N)
+      1
+      (cache '(NIL) (pack (char (hash N)) N)  # Memoize
+         (sum
+            '((I) (* (catalanRec I) (catalanRec (- N I 1))))
+            (range 0 (dec N)) ) ) ) )
+
+# Alternatively
+(de catalanAlt (N)
+   (if (=0 N)
+      1
+      (*/ 2 (dec (* 2 N)) (catalanAlt (dec N)) (inc N)) ) )
+
+# Test
+(for (N 0 (> 15 N) (inc N))
+   (tab (2 4 8 8 8)
+      N
+      " => "
+      (catalanDir N)
+      (catalanRec N)
+      (catalanAlt N) ) )